So, the following scenario:
I have plenty of polygons that are within another polygon, all in the same feature class. All of the polygons (the one overlaping the other ones as well as the ones being overlapped) have attributes which are important for my project. What I basically want is to erase those parts of the selected polygon (see screenshot below) that overlap with other polygons in the same feature class.

This is basically just reparing an error which went unnoticed for some time during an editing session and using the auto-complete-polygon option. The selected feature is supposed to be railtracks... you can surely guess what happened there. First step would be just to delete the overlaps, the rest I can do manually with the split-polygon tool.